rotational moment (that is the tendency for your body to rotate forward or backwards) is given by :

moment= force x perpendicular distance of line of force to pivot

where the force in this case is your own weight.

given this, if your centre of gravity is lower, and considering all else equal, your rotational moment is lower because the perpendicular distance of line of force to pivot is also lower ,so according to the equation above, it is harder to make you fall.